Many researchers have attempted to study the performance of the NLMS [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]} and to understand why it has superior performance over that of the LMS. In [1]}, closed-form expressions for the transient analysis and the steady-state
mean-square error (MSE) of the NLMS algorithm are developed but these expressions are in terms of multidimensional moments which
[1]} falls short of evaluation. Other prior work has attempted to evaluate these moments but the corresponding
analyses do not result in closed form performance expressions [2]}, [1]}, [3]}, or rely on strong assumptions.
Examples of these assumptions include the separation principle [4]}, [5]}, approximations [6]}, white input [3]}, [6]}, [8]}, specific structure of input regressor’s distribution [4]}, [21]}, small step size [4]}, long filters [6]}, approximate solutions using Abelian integrals [4]} and partial evaluation of moments [25]}.
